A small manufacturing firm uses approximately 3400 pounds of chemical dye per year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The ordering cost is $100 and inventory carrying cost is 51 cents per pound per year. D= 3400, S= 100, H=0.51a) The supplier has just announced that orders of 1000 pounds and more will be filled at a price of $2 per pound. Determine the order size that will minimizes the total cost.b) If the supplier offered a discount at 1500 pounds instead of 1000 pounds, what order size will minimize total cost?

Assignment Ch12(b)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO Order Quantity (Q)

An

nu

al C

os

t

(optimal order quantity)

SQ

DH

QTC

2

Ordering and Carrying Costs

Co

st

EOQ

TC with PD

TC without PD

PD

0 Quantity

Adding Purchasing costdoesn’t change EOQ

Ordering, Carrying, and Purchasing Costs

Co

st

0 Quantity

Price Discount

p1

p2

Co

st

EOQ0 Quantity

Total Cost Including Purchasing Cost

p1

p2

Co

st

EOQ0 Quantity

Price Breaks: EOQ Preferred

Co

st

Q0 Quantity

Price Breaks: Discount Point Preferred

Co

st

EOQ0 Quantity

Price Breaks: EOQ Preferred

A small manufacturing firm uses approximately 3400 pounds of chemical dye per year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The ordering cost is $100 and inventory carrying cost is 51 cents per unit per year. D=3400, S= 100, H=.51a) The supplier has just announced that orders of 1000 pounds and more will be filled at a price of $2 per pound.

The Problem: Part A

Q P0-999 3≥1000 2

115551.

)3400)(100(22

H

SDEOQ

DONE

A small manufacturing firm uses approximately 3400 pounds of chemical dye per year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The ordering cost is $100 and inventory carrying cost is 51 cents per unit per year. D=3400, S= 100, H=.51b) Determine the order size that will minimizes the total cost.If the supplier offered a discount at 1500 pounds instead of 1000 pounds, what order size will minimize total cost?

Q P0-... 3≥1500 2

1155EOQ

The Problem: Part B

b) If the supplier offered a discount at 1500 pounds instead of 1000 pounds, what order size will minimize total cost?

Q P0-... 3≥1500 2

D= 3400, S=100, H= .51

1155EOQ

TC = HQ/2 + SD/Q + PD

TC ( Q = 1155 , P = 3) = 0.51(1155)/2 + 100(3400)/1155 + 3(3400)TC = 294.5 + 294.5 + 10200 = 10789

TC ( Q = 1500 , P = 2) = 0.51(1500)/2 + 100(3400)/1500 + 2(3400)TC = 382.5+226.7 +6800 = 7409.2

The Problem: Part B